The 1940 census records were released by the U.S. National Archives in April 2012, and can be accessed online at 1940census.archives.gov. This website allows you full access to the 1940 census images, in addition to 1940 census maps and descriptions.
To find the person you're looking for in the 1940 census, the first step is to identify the appropriate enumeration district where that person lived. The data is not indexed, so you need to browse through the data looking for the name(s) for which you have an interest. The best way to find the appropriate enumeration district is to enter the state, county, city, street and cross street.
Click on Get Started → Start Your Search → then enter state, county, city, and street information, and then → Search. You'll then be given a list of enumeration districts and the chance to enter a cross street to further limit the enumeration districts returned. You may still get several enumeration districts returned even with a cross street. You will then have to browse through the data by the enumeration districts returned by either downloading the data or viewing it in full screen mode. As more than one enumeration district may be returned even if you specify a cross street, you may have to download several enumeration districts to finally find the relevant data.
The less specific you are with the data, you will have more enumeration districts returned, resulting in a much bigger search effort. There is an effort underway at the National Archives to index the data. A fully indexed database is available at Ancestry.com